The tonneau cover can increase the mpg, but only a bit. If you are driving in the same condition with that cover and without it, the difference between those two mpg values will be no greater than a couple of miles.
Variables that Determine Mpg
Your truck’s (or any automotive) fuel economy is determined by a certain value. In the US, Mpg (Miles per gallon) is used as the unit of fuel economy. It denotes the number of miles you can go by burning 1-gallon of fuel.
As expected, the fuel economy is not the same in all types of automotive. But this very economy also depends on the driving condition, road surface, terrain, payload, etc. To understand the Mpg better, a proper understanding of these conditions is needed.

1. Engine Type
The same truck model can be fitted with a different type of engine. Though the bodyweight of those trucks is the same, the fuel economy can vary. Some versions are fitted with a V8 engine. Those trucks consume more gas than any of their counterparts.
2. Average Speed & Driving mode
Most of the trucks now have different driving modes. The cruise speed can noticeably vary in these different modes. Besides, the suspension system and cruise controls also vary. The fuel consumption of your vehicle varies accordingly.
3. Payload
The payload of the vehicle is an obvious factor that contributes to fuel consumption. Greater payload or more number of passengers means the vehicle needs more fuel to run.
4. Driving Condition
Driving conditions can be defined as a combination of numerous variables. The condition of the road surface or terrain, inclination, weather, etc. variables come into play. So, if you want to compare fuel consumption, you have to make sure that the variables are almost the same in those cases.
Why Tonneau Cover?
The tonneau cover is important for protecting the payloads on the truck bed. Some tonneau covers come with special coatings that can repel water. These covers give the necessary protection against rain. Besides, tonneau covers are helpful to reduce the dust collection on the payload during a cruise.

How Tonneau Cover Improves Aerodynamics?
For the shape of a truck with an open bed, the air cannot pass uninterruptedly. Once passing air hit the cab, the upward airflow goes over it. But as the truck bed is not at the same height as the top of the cab, the upcoming airflow breaks and then hit the tailgate.
This phenomenon ultimately induces extra drag into the forward motion of the vehicle. If a tonneau cover is placed, the airflow won’t be able to hit the tailgate. As a result, some amount of drag is reduced. It improves the aerodynamic performance.

Does Tonneau Cover Improve Mpg?
Mpg depends on several factors, as illustrated before. Among them, the aerodynamic performance of the vehicle is a vital factor. As the drag is mitigated (by a small amount) by installing a tonneau cover, your truck requires less fuel, at least theoretically.
But if the performance is measured before and after installing the tonneau cover, the improvement can be hardly seen. In some cases, that improvement may hit a couple of miles. But in most of the scenario, it improves by a mile or so.

The tonneau cover can provide a surface for the airflow to pass on uninterruptedly. Still, the upcoming air induces a certain amount of drag. This drag cannot be mitigated noticeably. So, the aerodynamic performance remains almost the same.
Incorporate Other Factors Too
If you want to improve the mpg, depending solely on the tonneau cover is not the best decision. You have to do some required maintenance on the engine. Besides, you need to ensure proper greasing on the rotating parts, maintain the tires.
Depends On Weather
However, the mpg is largely dependent on the driving condition. You cannot get the mpg of a highway on an uphill surface. Besides, vehicles need more power in colder weather. So, you can get an improved mpg in warmer weather.
Wrapping Up
The tonneau cover is important to protect your belongings on the truck bed. To an extent, it also improves the aerodynamics of your truck which can result in better mpg of a couple of miles. But you cannot depend solely on this cover for getting an improved mpg. By the way, some people think that leaving the tailgate down saves gas though it is a debatable statement.
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